Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1367 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=c,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^4184 conjugacy classes — view the full character table.
| maximal subgroup of | #11985955, #11985956, #11985958, … |
| maximal normal subgroup of | #11985955, #11985956, #11985958, … |
| maximal quotient of | #11986038, #11986163, #11986966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12);